This disclosure relates to apparatus and methods for improving the precision of capacitive nanoscale measurements of pressure and other physical variables using micro electro mechanical systems, commonly referred to as MEMS. A particular focus is in developing features affording linear performance characteristics of such devices, which may be further varied by application of electrostatic, thermal, or physical displacement biasing. Another focus is in developing novel structural component elements designed to simplify the manufacture of MEMS devices having the desired features.
The use of MEMS devices for measurement of pressure and other physical variables is known, for example, from U.S. Pat. No. 7,721,587 and the prior art references cited therein. It is well known to researchers in the area of micro and nano-electromechanical systems (M/NEMS) that mechanical performance strongly depends on geometric and material properties. These fabricated properties are difficult to predict and difficult to measure. The problem with prediction is that, given any fabrication recipe, the geometric and material properties of the devices that result from that recipe will vary between fabrication facilities, between fabrication runs, and even across a given wafer itself. A problem with many measurement methods is that they often yield uncertainties that are of the same order as the property being measured.
Regarding material properties, for a given displacement, Young's modulus is often used to determine force in MEMS by Hooke's law. However, the Young's modulus of fabricated MEMS devices is often unknown. Although many in the field use lookup tables to determine the Young's modulus, such values are usually averages of measurements that vary by 10 percent or more. Since there is currently no standard for measuring Young's moduli, the true accuracy of such measurements is unknown. It has been shown that standard overetch errors in fabrication can increase system stiffness as high as 98%. Including the uncertainty in Young's modulus increases the relative error in stiffness to 188%. Thus, there remains a need for MEMS measurement devices that can be reliably calibrated and operate on a linear slope to simplify the calibration and scaling of the movement of the MEMS device in relation to the variable sought to be measured.